**The fourth meeting on hot subdwarf stars ** and related objects Progress in the asteroseismic analysis of the pulsating sdB star PG 1605+072 Valérie Van Grootel(Laboratoire d’Astrophysique de Toulouse, France) S. Charpinet (Laboratoire d’Astrophysique de Toulouse)G. Fontaine and P. Brassard (Université de Montréal)

**Outline** 1. Introduction to the pulsating sdB star PG 1605+072 • Photometric observations • Spectroscopic observations • Is PG 1605+072 a fast rotator ? 2. Models and Method for the asteroseismic analysis 3. Asteroseismic analysis : hypothesis of a slow rotation4. Asteroseismic analysis : hypothesis of a fast rotation5. Comparison between the two hypotheses 6. Conclusion and raising questions

**Introduction to PG 1605+072** • “PG 1605+072, a unique pulsating sdB star” • > Koen et al. (1998a) : discovery of a rapidly pulsating sdB star (EC14026 class) with an unusually rich pulsation spectrum and long periods (200 - 600 s) • > Kilkenny et al. (1999), multi-site campaign (180h data over 15 days - 1Hz resolution) : • 44 pulsation periods useful for asteroseismology (28 totally reliable) • > van Spaandonk et al. (2008), from 4-days campaign @ CFHT (~ 4Hz resolution) : • 46 pulsation periods useful for asteroseismology, including 38 common with Kilkenny • Light curve particularities • no real sinusoidal form • no clear pseudo-period • very high amplitudes for dominant modes : • f1 :A64 mmags (~2.5%) • f2 to f5 : A 1% • no sign of companion

**Introduction to PG 1605+072** • Spectroscopic observations : atmospheric parameters • Heber et al. (1999), Keck-HIRES (0.1Å), averaged LTE with metals and NLTE models: • Teff 32 300 300 K • log g 5.25 0.1 • G. Fontaine, 2.3-m Kitt Peak (9Å), NLTE: • Teff 32 940 450 K • log g 5.31 0.08 • G. Fontaine, 6-m MMT (1Å), NLTE: • Teff 32 660 390 K • log g 5.26 0.05 Averaged mean value : Teff 32 630 600 K and log g 5.273 0.07 Very low surface gravity for an EC14026 star Evolved state beyond TA-EHB ? Very high-mass sdB star ?

**Figure from Heber et al. (1999)** Introduction to PG 1605+072 • Is PG 1605+072 a fast rotator ? > Line broadening measured by Heber et al. (1999) : 39 km s-1 (unusually high for a sdB star) • > Rotational broadening ? Veq sin i 39 km s-1 • PG 1605+072 is a fast rotator, as suggested by Kawaler (1999). This explains the complexity of the pulsation spectrum, by the lift of (2l+1)-fold degeneracy in frequencies • > Pulsational broadening ? • Kuassivi et al. (2005), FUSE spectra : Doppler shift of 17 km s-1 • O’Toole et al. (2005), MSST : 20 pulsation modes by RV method, amplitudes between 0.8 and 15.4 km s-1 • Veq sin i 39 km s-1 origin of the complexity of the pulsation spectrum ?

**Introduction to PG 1605+072** • Suggestion from P. Brassard : Lots of low-amplitude pulsation frequencies are due to 2nd- and 3rd-order harmonics and nonlinear combinations of high amplitude frequencies. • All the pulsation spectrum can be reconstructed from 22 basic frequencies, including the highest amplitude ones • Some of these can be interpreted as very close frequency multiplets (slow rotation) • 14 independent pulsation modes remain to test the idea of a slow rotation for PG 1605+072, in a seismic analysis by comparison with kl,m0 theoretical frequencies

**Envelope** Core 2. Models and Method for asteroseismology • > 2nd generation models • static envelope structures; central regions (e.g. convective core) hard ball • include detailed envelope microscopic diffusion (nonuniform envelope Fe abundance) • 4 input parameters : Teff, log g, M*, envelope thickness log (Menv/M*) • > 3rd generation models • complete static structures; including detailed central regions description • include detailed envelope microscopic diffusion (nonuniform envelope Fe abundance) • input parameters : total mass M*, envelope thickness log (Menv/M*), convective core size log (Mcore/M*), convective core composition He/C/O (under constraint COHe 1) With 3rd generation models, Teff and log g are computed a posteriori Atmospheric parameters from spectroscopy are used as external constraints for seismic analysis

**;** 2. Models and Method for asteroseismology The forward modeling approach for asteroseismology • Fit directly and simultaneously all observed pulsation periods with theoretical ones calculated from sdB models, in order to minimize • The rotational multiplets (lifting (2l+1)-fold degeneracy) are calculated by 1st order perturbative approach : • Efficient optimization algorithms are used to explore the vast model parameter space in order to find the minima of S2 i.e. the potential asteroseismic solutions • Results : • Structural parameters of the star (Teff, log g, M*, envelope thickness, etc.) • Identification (k,l,m) of pulsation modes (with or without external constraints) • Internal dynamics Ω(r)

**> Search parameter space :** • 0.30 M*/Ms 1.10 (Han et al. 2002, 2003) • 6.0 log (Menv/M*) 1.8 • 0.40 log (Mcore/M*) 0.02 • 0 X(C+O) 1 Under the constraints Teff 32 630 600 K and log g 5.273 0.07 3. Asteroseismic analysis : Hypothesis of a slow rotation • Search the model whose kl,m0 theoretical frequencies best fit the 14 observed ones • (other frequencies can be interpreted as very close frequency multiplets, or harmonics, or nonlinear combinations) Hypotheses : > Forbid l3 associations for visibility reasons (Randall et al. 2005) Best-fit model by optimization procedure : • M* 0.7624 Ms • log (Menv/M*) 2.6362 • log (Mcore/M*) 0.0240 • X(C+O) 0.45 ; X(He) 0.65 Teff 32 555 K log g 5.2906 Period fit : S2 ~ 3.71 P/P ~ 1.03% or P ~ 4.45 s (relatively good fit)

**A ~ 0.70 %** A ~ 0.56% A ~ 0.91% A ~ 0.51% 3. Asteroseismic analysis : Hypothesis of a slow rotation • Period fit and mode identification

**not consistent with external spectroscopic constraints** > on M* and log (Menv/M*) Mcore and X(C+O) are interdependant and not well defined (lack of sensitivity of pulsation modes to central regions) not consistent with external spectroscopic constraints quite well defined by pulsation spectrum and external spectroscopic constraints 3. Asteroseismic analysis : Hypothesis of a slow rotation • Comments on structural parameters > on X(C+O) and log (Mcore/M*) We find a very-high mass and thick envelope model on EHB for PG 1605+072, consistent with the hypothesis of a slow rotation

**4. Asteroseismic analysis : Hypothesis of a fast rotation** • Search the model whose klm theoretical frequencies best fit the 28 “totally reliable” observed ones (Kilkenny et al. 1999) Kolmogorov-Smirnov test (gives the credibility of regular spacings in pulsation spectrum) ~ 90.4 Hz Prot ~ 11 000 s (~ 3 h) Remark : our 1st order perturbative approach for rotation is valid up to 2.5h (Charpinet et al. 2008)

**> Search parameter space :** • 0.30 M*/Ms 1.10 (Han et al. 2002, 2003) • 6.0 log (Menv/M*) 1.8 • 0.40 log (Mcore/M*) 0.02 • 0 X(C+O) 1 • solid rotation : 8000 s Prot 16000s Under the constraints Teff 32 630 600 K and log g 5.273 0.07 > Forbid l3 associations for visibility reasons (Randall et al. 2005) 4. Asteroseismic analysis : Hypothesis of a fast rotation Best-fit model by optimization procedure : • M* 0.7686 Ms • log (Menv/M*) 2.7114 • log (Mcore/M*) 0.0722 • X(C+O) 0.28 ; X(He) 0.72 • Prot 11 075 s 3.076 h Teff 32 723 K log g 5.2783 Period fit : S2 ~ 8.04 P/P ~ 0.21% or P ~ 0.87 s (excellent fit)

**All f1 to f8 : l 2** 4. Asteroseismic analysis : Hypothesis of a fast rotation Period fit and mode identification

**not consistent with external spectroscopic constraints** Mcore and X(C+O) are interdependant and not well defined (lack of sensitivity of pulsation modes to central regions) > on M* and log (Menv/M*) not consistent with external spectroscopic constraints quite well defined by pulsation spectrum and external spectroscopic constraints 4. Asteroseismic analysis : Hypothesis of a fast rotation • Comments on structural parameters > on X(C+O) and log (Mcore/M*) A very-high mass model and thick envelope on EHB is found for PG 1605+072, consistent with the hypothesis of a fast rotation (~ 3 h)

** (log (Mcore/M*) 0.0240)** • (X(C+O) 0.45 ; X(He) 0.65) • (log (Mcore/M*) 0.0722) • (X(C+O) 0.28 ; X(He) 0.72) • Star structure is very well defined(except core parameters) • Star rotation not. Independent problems ! Remark : all the m0 identified in the analysis with rotation belong to the 14 “basic frequencies” (NOT a hypothesis !) 5. Asteroseismic analysis : Comparison between the 2 hypotheses Fast rotation Slow rotation • M* 0.7686 Ms • log (Menv/M*) 2.7114 • Prot 11 075 s 3.076 h • M* 0.7624 Ms • log (Menv/M*) 2.6362 Teff 32 555 K log g 5.2906 Teff 32 723 K log g 5.2783 Similarity of model found in both cases ! (associated errors still have to be calculated)

**6. Conclusion and raising questions** • Conclusion : • We have found very high-mass and thick envelope model for PG1605+072 from asteroseismology • Model consistent with a star on the EHB : • Teff ~ 32 600 K • log g ~ 5.285 • M*~ 0.765 Ms • log (Menv/M*) ~ 2.65 • Raising questions : • Is PG 1605+072 a fast rotator ? (asteroseismology cannot help on this question) Line broadening rotational broadening + pulsational broadening in which proportions ? • What is the formation channel for PG 1605+072 ??? • PG 1605+072 is most probably a single star • We are “in the tail” of all formation channels ! (Han et al. 2002, 2003). Even “two WD merger” scenario

**Validity of the 1st order perturbative approach** • Evaluation of higher orders effects from polytropic (N3) model of sdB star, with full treatment of rotation (work of D. Reese & F. Lignières) 2nd order 3rd order higher orders • Rotation period greater than ~ 9 h : 1st order completely valid • Rotation period to ~ 2.5 h : corrections due to high orders (mainly 2nd order) have the same scale than the accuracy of asteroseismic fits (10 - 15 Hz) Conclusion : 1st order perturbative approach valid for our purposes